It doesn't get much simpler than this circuit. Four components counting the battery!
How can an LED be illuminated by a 1.5V circuit, when the forward voltage of an LED is about 2V? The LM3909 uses the 100uF capacitor as a charge reservoir, building up a voltage of about 2V before discharging the cap through the LED.
This circuit is used in emergency flashlights on airplanes and in other public places. Though you may not have known it till now, the LM3909 is everywhere!